Kelly is gluing rectangular cards in her scrapbook. Each card has an area of 24 square inches and the length is 2 inches more than the width. If x represents the width of each card, select all of the equations that could be used to find the length and width of her cards.

Question

Mathematics

Alexis Krause

22 November, 07:57

Kelly is gluing rectangular cards in her scrapbook. Each card has an area of 24 square inches and the length is 2 inches more than the width. If x represents the width of each card, select all of the equations that could be used to find the length and width of her cards.

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Answers (1)

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Glenn · Answer 1

The equation would be (w+2) (w) = 24, the width would be 4 and the length would be 6.

We find the area of a rectangle by multiplying its length and width:

A = lw

The length is 2 more than the width, or l = w+2:

A = (w+2) (w)

24 = (w+2) (w)

Multiplying this through, we have:

24 = w² + 2w

We want the equation set equal to 0 to solve it, so subtract 24 from both sides:

24 - 24 = w² + 2w - 24

0 = w² + 2w - 24

This is easily factorable, as 6 (-4) = - 24 and 6 + - 4 = - 2:

0 = (w+6) (w-4)

Using the zero product property, we know either w+6=0 or w-4 = 0, so w=-6 or w=4. A negative width makes no sense, so w = 4. This means l = w+2 = 4+2 = 6.